Math 220 Assignment

November 2, 2001

Due Monday, November 5

1. What is the length of the line segment from the point (2, -1, 1) to the point (4, -4, 7) ?

2. What is the angle at the point (0, 1, -1) in the triangle whose vertices are that point, the point (-1, 3, 1), and the point (3, 7, -3) ?

3. Let M be the 2 \times 3 matrix

   M  =

   ( 3  0 -1 3 -2 0 )

   ,

   and let f be the linear function from R^{3} to R^{2} that is defined by f(x) = M x. Find a basis of the kernel of f consisting of vectors of length 1.

4. Find a basis consisting of mutually perpendicular vectors for the plane in R^{3} defined by the linear equation

   2 x - y + 2 z  =  0  .

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